Connectionism 2011 and 2 in panel A of Figure 8.8), it is in an attractor basin and
will tend to stay there unless disturbed. If it is on a hill (be-
tween 1 and 2), any slight movement in either direction will
cause it to escape its current location and move to an adjacent
attractor.
One strength of this portrayal is that it does a good job of
creating a sense of how attractors vary in robustness. The
breadth of a basin indicates the diversity of trajectories in
phase space that are drawn into it. The broader is the basin
(B-1 in Figure 8.8), the more trajectories are drawn in. The
narrower the basin (B-2), the closer the ball has to come to its
focal point to be drawn to it. The steepness of the valley indi-
cates how abruptly a trajectory is drawn into it. The steeper
the slope of the wall (B-2), the more sudden is the entry of a
system that encounters that basin.
The depth of the valley indicates how firmly entrenched
the system is, once drawn into the attractor. Figure 8.8, panel
C, represents a system of attractors with fairly low stability
(the valleys are shallow). One attractor represents a stable
situation (valley 1), whereas the others are less so. It will take
a lot more “energy” to free the ball from valley 1 than from
the others.
There is a sense in which both breadth and depth suggest
that a goal is important. Breadth does so because the system
is drawn to the attractor from widely divergent trajectories.
Depth does so because the system that has been drawn into
the basin tends to stay there.
A weakness of this picture, compared to a phase-space
portrait, is that it is not as good at giving a sense of the erratic
motion from one attractor to another in a multiple-attractor
system. You can regain some of that sense of erratic shifting,
however, if you think of the surface in Figure 8.8 as a tam-
bourine being continuously shaken (Figure 8.8, panel D).
Even a little shaking causes the ball to bounce around in its
well and may jostle it from one well to another, particularly
if the attractors are not highly stable. An alternative would be
to think of the ball as a jumping bean. These two characteri-
zations would be analogous to jostling from situational influ-
ences and jostling from internal dynamics, respectively.
Goals as Attractors
The themes of dynamic systems thinking outlined here
have had several applications in personality–social and
even clinical psychology (Hayes & Strauss, 1998; Mahoney,
1991; Nowak & Vallacher, 1998; Vallacher & Nowak, 1997).
Perhaps the easiest application of the attractor concept to
self-regulatory models is to link it with the goal concept. In-
deed, alert readers will have noticed that we used the same
metaphor—gravity and antigravity—in describing both the
goal construct at the beginning of the chapter and in describ-
ing the attractor concept just earlier.
As we said at the beginning of the chapter, goals are points
around which behavior is regulated. People spend much of
their time doing things that keep their behavior in close prox-
imity to their goals. It seems reasonable to suggest, then, that
a goal represents a kind of attractor. Further, if a goal is an at-
tractor, it seems reasonable that an antigoal would represent a
repeller.
This functional similarity between the goal construct and
the attractor basin is very interesting. However, the similarity
exists only with respect to the end product—that is, main-
taining proximity to a value (or remaining distant from a
value). The two views make radically different assumptions
about the presence or absence of structure underlying the
functions. The feedback model assumes a structure underly-
ing and supporting the process, whereas the dynamic systems
model does not necessarily incorporate such an assumption.CONNECTIONISMA related set of questions about the role of central control
processes is raised by the literature of connectionism. Con-
nectionist models simulate thought processes in networks of
artificial units in which “processing” consists of passing acti-
vation among the units. As in neurons, the signal can be exci-
tatory or inhibitory. Energy passes in only one direction
(though some networks have feedback links). Processing
proceeds entirely by the spread of activation—there is no
higher order executive to direct traffic. In a distributed con-
nectionist network, knowledge is not represented centrally, as
nodes of information. Rather, knowledge is represented in
terms of the patternof activation of the network as a whole
(Smith, 1996).
In networks with feedback relations, once the system re-
ceives input, the pattern of weights and activations is updated
repeatedly across many cycles. Thus, modifications or up-
dates are made iteratively throughout the network, both with
respect to activation in each node and the weighting func-
tions. Gradually, the various values asymptote, and the sys-
tem “settles” into a configuration. The settling reflects the
least amount of overall error the system has been able to cre-
ate, given its starting inputs and weights.Multiple Constraint SatisfactionA useful way to think about this process is that the system si-
multaneously satisfies multiple constraints that the elements
create on each other (Thagard, 1989; see also Kelso, 1995).